By using the technique of real analysis,the parameter conditions for Hilberttype series operator and integral operator T_(1)(˜a)(x)=∑∞n=1 K(n,x)a_(n),T_(2)(f)_(n)=∫+∞0 K(n,x)f(x)dx.bounded with homogeneous kernels...By using the technique of real analysis,the parameter conditions for Hilberttype series operator and integral operator T_(1)(˜a)(x)=∑∞n=1 K(n,x)a_(n),T_(2)(f)_(n)=∫+∞0 K(n,x)f(x)dx.bounded with homogeneous kernels are discussed.The necessary and sufficient conditions for T_(1):l^(α)_(p)→L^(β)_(p)^((1−p))p(0,+∞)and T_(2):L_(q)^(β)(0,+∞)→l^(α(1−q))_(q)bounded are obtained,and their norm expressions are established under certain conditions.展开更多
In this paper, by introducing some parameters and estimating the weight coefficient, we give a new Hilbert’s inequality with the integral in whole plane and with a non-homogeneous and the equivalent form is given as ...In this paper, by introducing some parameters and estimating the weight coefficient, we give a new Hilbert’s inequality with the integral in whole plane and with a non-homogeneous and the equivalent form is given as well. The best constant factor is calculated by the way of Complex Analysis.展开更多
Through using weight function, we give a new Hilbert-type integral inequality with two independent parameters and two pair of conjugate exponents, which is a best extension of a Hilbert-type integral inequality with t...Through using weight function, we give a new Hilbert-type integral inequality with two independent parameters and two pair of conjugate exponents, which is a best extension of a Hilbert-type integral inequality with the homogeneous kernel of 0-degree. The equivalent form, the reverses and some particular results are considered.展开更多
By introducing some parameters and estimating the weight function,we obtain an extension of reverse Hilbert-type inequality with the best constant factor.As applications,we build its equivalent forms and some particul...By introducing some parameters and estimating the weight function,we obtain an extension of reverse Hilbert-type inequality with the best constant factor.As applications,we build its equivalent forms and some particular results.展开更多
In this paper, we establish several new Hilbert-type inequalities with a homogeneous kernel, involving arithmetic, geometric, and harmonic mean operators in both integral and discrete case. Such inequalities are deriv...In this paper, we establish several new Hilbert-type inequalities with a homogeneous kernel, involving arithmetic, geometric, and harmonic mean operators in both integral and discrete case. Such inequalities are derived by virtue of some recent results regarding general Hilbert-type inequalities and some well-known classical inequalities. We also prove that the constant factors appearing in established inequalities are the best possible. As an application, we consider some particular settings and compare our results with previously known from the literature.展开更多
In this paper it is shown that a new Hilbert-type integral inequality can be established by introducing two parameters m（m ∈ N） and λ（λ 0）.And the constant factor expressed by the Bernoulli number and π is pro...In this paper it is shown that a new Hilbert-type integral inequality can be established by introducing two parameters m（m ∈ N） and λ（λ 0）.And the constant factor expressed by the Bernoulli number and π is proved to be the best possible.And then some important and especial results are enumerated.As applications,some equivalent forms are given.展开更多
In this article we discuss the explicit solvability of both Schwarz boundary value problem and Riemann-Hilbert boundary value problem on a half hexagon in the complex plane. Schwarz-type and Pompeiu-type integrals are...In this article we discuss the explicit solvability of both Schwarz boundary value problem and Riemann-Hilbert boundary value problem on a half hexagon in the complex plane. Schwarz-type and Pompeiu-type integrals are obtained. The boundary behavior of these operators is discussed. Finally, we investigate the Schwarz problem and the Riemann-Hilbert problem for inhomogeneous Cauchy-Riemann equations.展开更多
基金Supported by Guangdong Basic and Applied Basic Research Foundation Natural Science Foundation(Grant No.2021A1515010055)Guangzhou Science and Technology Plan Project(Grant No.202102080177).
文摘By using the technique of real analysis,the parameter conditions for Hilberttype series operator and integral operator T_(1)(˜a)(x)=∑∞n=1 K(n,x)a_(n),T_(2)(f)_(n)=∫+∞0 K(n,x)f(x)dx.bounded with homogeneous kernels are discussed.The necessary and sufficient conditions for T_(1):l^(α)_(p)→L^(β)_(p)^((1−p))p(0,+∞)and T_(2):L_(q)^(β)(0,+∞)→l^(α(1−q))_(q)bounded are obtained,and their norm expressions are established under certain conditions.
文摘In this paper, by introducing some parameters and estimating the weight coefficient, we give a new Hilbert’s inequality with the integral in whole plane and with a non-homogeneous and the equivalent form is given as well. The best constant factor is calculated by the way of Complex Analysis.
基金Project supported by the Natural Science Foundation of the Institutions of Higher Learning of Guangdong Province (GrantNo.05Z026)the Natural Science Foundation of Guangdong Province (Grant No.7004344)
文摘Through using weight function, we give a new Hilbert-type integral inequality with two independent parameters and two pair of conjugate exponents, which is a best extension of a Hilbert-type integral inequality with the homogeneous kernel of 0-degree. The equivalent form, the reverses and some particular results are considered.
文摘By introducing some parameters and estimating the weight function,we obtain an extension of reverse Hilbert-type inequality with the best constant factor.As applications,we build its equivalent forms and some particular results.
文摘In this paper, we establish several new Hilbert-type inequalities with a homogeneous kernel, involving arithmetic, geometric, and harmonic mean operators in both integral and discrete case. Such inequalities are derived by virtue of some recent results regarding general Hilbert-type inequalities and some well-known classical inequalities. We also prove that the constant factors appearing in established inequalities are the best possible. As an application, we consider some particular settings and compare our results with previously known from the literature.
基金Supported by the Project of Scientific Research Fund of Hunan Provincial Education Department (GrantNo.09C789)
文摘In this paper it is shown that a new Hilbert-type integral inequality can be established by introducing two parameters m（m ∈ N） and λ（λ 0）.And the constant factor expressed by the Bernoulli number and π is proved to be the best possible.And then some important and especial results are enumerated.As applications,some equivalent forms are given.
文摘In this article we discuss the explicit solvability of both Schwarz boundary value problem and Riemann-Hilbert boundary value problem on a half hexagon in the complex plane. Schwarz-type and Pompeiu-type integrals are obtained. The boundary behavior of these operators is discussed. Finally, we investigate the Schwarz problem and the Riemann-Hilbert problem for inhomogeneous Cauchy-Riemann equations.
